Monitoring of Distillation Column Based on Indiscernibility Dynamic Kernel PCA

Torque tube is widely used on the offshore platform, and its quality plays an important role on the security of offshore platform. The cold bending forming process for torque tube production is nonlinear and dynamic seriously, with the fault types varied and complex, so the traditional PCA cannot get a good effect in the fault detection of cold bending forming. In this paper, a fault detection method based on dynamic kernel principal component analysis (DKPCA) algorithm is introduced to detect the faults of the cold bending forming. Eleven process variables were sampled from the actual manufacture process and used for fault diagnosis. PCA and DKPCA are used to carry out fault detection on the cold bending forming process, and the results show that the effect of DKPCA for fault detection is better than that of PCA. DKPCA can improve the detection effect greatly due to its advantage in nonlinear and dynamic characteristics, which can be applied widely in actual process.

The practical application of traditional data‐driven techniques for process monitoring encounters significant challenges due to the inherent nonlinear and dynamic nature of most industrial processes. Aiming at the problem of nonlinear dynamic process monitoring, a novel fault detection method based on dynamic kernel principal component analysis combined with weighted structural difference (DKPCA‐WSD) is proposed in this paper. Initially, the proposed method leverages a sophisticated nonlinear transformation to project the augmented matrix of the original input data into a high‐dimensional feature space, thereby facilitating the establishment of a DKPCA model. Subsequently, the WSD statistic is computed, utilizing a widely known sliding window technique, to quantify the mean and standard deviation differences across data structures. Ultimately, the WSD statistic is utilized for fault detection, completing the process monitoring task. By integrating the capability of DKPCA to capture nonlinear dynamic characteristics with the effectiveness of the WSD statistic in mitigating the impact of non‐Gaussian data distributions, DKPCA‐WSD significantly enhances the monitoring performance of traditional DKPCA in nonlinear dynamic processes. The proposed method is evaluated through a numerical case exhibiting nonlinear dynamic behaviors and a simulation model of a continuous stirred tank reactor. A comparative analysis with conventional methods, including principal component analysis (PCA), dynamic principal component analysis, KPCA, PCA similarity factor (SPCA), DKPCA, and moving window KPCA (MWKPCA), demonstrates that DKPCA‐WSD outperforms traditional fault detection techniques in nonlinear dynamic processes, offering a substantial improvement in monitoring performance.

This paper proposes dynamic kernel principal components analysis (DKPCA) approach to bioprocesses monitoring. The basic idea of KPCA is to map the input data into a feature space first via a nonlinear mapping, and then perform a linear PCA in feature space F . The dynamic kernel matrix of DKPCA can capture the nonlinearity and the dynamics of bioprocesses. The proposed method was applied to the fault detection and diagnosis of a simulation benchmark of a biological treatment process. The simulation results clearly show the effectiveness of the proposed approach.

This paper presents a novel Gabor-based kernel Principal Component Analysis (PCA) method by integrating the Gabor wavelet representation of face images and the kernel PCA method for face recognition. Gabor wavelets first derive desirable facial features characterized by spatial frequency, spatial locality, and orientation selectivity to cope with the variations due to illumination and facial expression changes. The kernel PCA method is then extended to include fractional power polynomial models for enhanced face recognition performance. A fractional power polynomial, however, does not necessarily define a kernel function, as it might not define a positive semidefinite Gram matrix. Note that the sigmoid kernels, one of the three classes of widely used kernel functions (polynomial kernels, Gaussian kernels, and sigmoid kernels), do not actually define a positive semidefinite Gram matrix either. Nevertheless, the sigmoid kernels have been successfully used in practice, such as in building support vector machines. In order to derive real kernel PCA features, we apply only those kernel PCA eigenvectors that are associated with positive eigenvalues. The feasibility of the Gabor-based kernel PCA method with fractional power polynomial models has been successfully tested on both frontal and pose-angled face recognition, using two data sets from the FERET database and the CMU PIE database, respectively. The FERET data set contains 600 frontal face images of 200 subjects, while the PIE data set consists of 680 images across five poses (left and right profiles, left and right half profiles, and frontal view) with two different facial expressions (neutral and smiling) of 68 subjects. The effectiveness of the Gabor-based kernel PCA method with fractional power polynomial models is shown in terms of both absolute performance indices and comparative performance against the PCA method, the kernel PCA method with polynomial kernels, the kernel PCA method with fractional power polynomial models, the Gabor wavelet-based PCA method, and the Gabor wavelet-based kernel PCA method with polynomial kernels.

The Internet environmenthas provided massive data to the actualindustrial production process. It not only has large amounts of databut also has a high data dimension, which brings challenges to thetraditional statistical process monitoring. Aiming at the nonlinearityand dynamics of industrial large-scale high-dimensional data, an efficientiterative multiple dynamic kernel principal component analysis (IMDKPCA)method is proposed to monitor the complex industrial process withsuper-large-scale high-dimensional data. In KPCA, a new KKT matrix is first created by using kernel matrix K. According to theproperties of the symmetric matrix, the newly constructed matrix hasthe same eigenvector as the original matrix K; hence, each columnof the matrix K can be used as the input sample of the iteration algorithm.After iterative operation, the kernel principal component can be deducedfleetly without the eigen decomposition. Because the kernel matrixis not stored in the algorithm beforehand, it can effectively reducethe computation complexity of the kernel. Especially for a tremendousdata scale, the traditional eigen decomposition technology is no longerappropriate, yet the presented method can be solved quickly. The autoregressivemoving average (ARMA) time series model and kernel principal componentanalysis (KPCA) are combined to build the IDKPCA model for dealingwith the dynamics and nonlinearity in the industrial process. Eventually,it is applied to monitor faults in the penicillin fermentation processand compared with MKPCA to certify the accuracy and applicabilityof the proposed method.

Network operators are now facing bandwidth outages as well as a growing pressure to ensure good Quality of Service (QoS). An important practical issue for network service providers is to pay close attention to the load changes of network traffic, in particular, the stationary increase of load from a normal demand. Many network monitoring applications and performance analysis tools are based on the study of an aggregate measure of network traffic, e.g. number of packets in transit (NPT), which is a long-term univariate time series. To classify this type of network traffic data and detect any increase of network source load, we propose a dynamic principal component analysis (PCA) method, first to extract data features and then to detect a stationary load increase of network traffic. The proposed detection schemes are based on either the major or the minor principal components of network traffic data. To demonstrate the applications of the proposed feature extraction method and the detection schemes, we applied them to network traffic data simulated from the packet switching network (PSN) model. Additionally, we propose a combined detection scheme that uses both the major and the minor principal components. The proposed detection schemes, based on dynamic PCA, show enhanced performance in detecting an increase of network load for the simulated network traffic data. These results offer a new feature extraction method based on dynamic PCA that creates additional feature variables for event detection in a univariate time series.

The control of large-scale industrial systems has several criteria, such as ensuring high productivity, low production costs and the lowest possible environmental impact. These criteria must be established for all subsystems of the large-scale system. This study is devoted to the development of a hierarchical control system that meets several of these criteria and allows for the separate optimization of each subsystem. Multicriteria optimization is based on the processing of data characterizing production processes, which makes it possible to organize a multidimensional statistical control process. Using neural networks to model the technological processes of subsystems and the method of dynamic principal component analysis (DPCA) to reduce the dimensionality of control problems allows us to find more efficient solutions. Using the example of a two-level hierarchy, we showed a variant of the connection between two subsystems by parameters.

This paper presents and compares model-based and data-driven fault detection approaches for coal mill systems. The first approach detects faults with an optimal unknown input observer developed from a simplified energy balance model. Due to the time-consuming effort in developing a first principles model with motor power as the controlled variable, data-driven methods for fault detection are also investigated. Regression models that represent normal operating conditions (NOCs) are developed with both static and dynamic principal component analysis and partial least squares methods. The residual between process measurement and the NOC model prediction is used for fault detection. A hybrid approach, where a data-driven model is employed to derive an optimal unknown input observer, is also implemented. The three methods are evaluated with case studies on coal mill data, which includes a fault caused by a blocked inlet pipe. All three approaches detect the fault as it emerges. The optimal unknown input observer approach is most robust, in that, it has no false positives. On the other hand, the data-driven approaches are more straightforward to implement, since they just require the selection of appropriate confidence limit to avoid false detection. The proposed hybrid approach is promising for systems where a first principles model is cumbersome to obtain.

In the recognition of digital modulation signals, extracting the characteristics that more easily distinguish the source signals, and have better performance of the signal, the source signals can be identified by using these characteristics. This paper optimized the original 20 features using orthogonal experiment method, and then identified the signals by the neural network, finally compared its results with that of PCA(principal component analysis) and KPCA(kernel principal component analysis) methods. Experimental results show that orthogonal experiment method in Gaussian and multipath environment can optimize the selection of the features to achieve higher recognition rate than the original features. Orthogonal experiment method has a better ability than PCA and KPCA methods in the optimal choice of these 20 characteristics.

Performance Monitoring of MPC Based on Dynamic Principal Component Analysis

Many researches have been carried out on incipient fault prediction technology for key machine components (such as bearings) based on historical and real-time condition monitoring data. However, there is still lack of well-understood systematic methodologies for detecting incipient fault for rotating machines. Based on machine learning technology, this paper studies an incipient fault prediction model applying with wavelet packet decomposition and dynamic kernel principal component analysis (WPD-DKPCA) to meet the needs of engineering applications. The incipient fault prediction WPD-DKPCA model, which does not require knowledge on equipment structure and failure mechanisms, only requires normal state data of the machine, and incipient fault prediction can be achieved through self-learning. Run-to-failure experimental data and engineering case data have been used to verify the constructed model, and the verification results show that the constructed model can reliably and accurately detect an incipient bearing fault. Comparisons of fault prediction effects prove that using T2 statistic monitoring can detect upcoming faults of machines much earlier than Kurtosis and Root Mean Square (RMS).

Locality Preserving Projections (LPP) is a linear projective map that optimally preserves the neighborhood structure of the data set. Though LPP has been applied in many fields, it has limits to solve recognition problem. Thus, a new palmprint recognition method is proposed based on Kernel Locality Preserving Projections (KLPP). Different from LPP method, KLPP not only describes the nonlinear correlations between pixels, but also preserves the local structure of the palmprint image space. In this way, the unwanted variations resulting from in lighting may be eliminated or reduced. We compare our proposed approach with Principal Component Analysis (PCA), LPP and Kernel Principal Component Analysis (KPCA) methods on PolyU palmprint database. Experiment results demonstrate that KLPP achieves better recognition rate as the dimension of the palmprint subspace changes.

Background Availability of numerous oil deposits with a wide variety of the conditions of occurrence, reservoir properties and physical-chemical properties of fluids makes important the need of grouping of development objects and identification of relatively uniform groups by certain criteria. Grouping allows to define similarities and differences between deposits in determining development objects, and to substantiate systems of development. Analysis of large data sets on objects characterized by the measured or estimated parameters is labor-intensive, requiring a lot of time and effort, so there is a question of dimension reduction, i.e. of reducing the original data set to a smaller number of parameters, and grouping of objects into relatively uniform groups. Here the parameters can be selected from the original ones or obtained by calculation and conversion (with the least loss of information about the objects under study). An effective tool of analysis that can help in this matter is the method of principal component analysis. Aims and Objectives Apply the method of principal component analysis to reduce the number of parameters which define objects of study, so that to find effective ways to develop new oil and gas deposits, and fast and correct solution of practical problems through the use of gained summary experience and assessment of similarities and differences of oil and gas reservoirs by combinations of geological-field attributes. Methods The problem of ranking oil deposits in Western Siberia, is solved by the method of principal component analysis, which is a linear transformation of features in a new set of «independent» random values, which are arranged in descending order of their variances, and the main components are determined by the eigenvectors of the correlation matrix obtained based on input parameters characterizing the objects under investigation. Having selected the components that comprise the bulk of the variances, one can calculate them for different types of objects and classify by clusterable points. Grouping of objects of research was carried out using built-in functions of computer statistics programs (a system of statistical analysis Statistica, analytical applications for Microsoft Excel XLStat). The same calculation was performed on the basis of the theory of mathematical statistics. The calculation results coincided. Results The method of principal component analysis allowed selection from the original data set comprising 50 research objects characterized by 12 parameters of six relatively uniform groups using only 4 factors (principal components) which, however, contain much more information than the individual parameters. As a result of the carried out analysis data were systematized and the dimension of the initial population (transition from multidimensional space to the four-dimensional) was reduced, with no significant loss of information about research objects. Conclusion Based on the proposed algorithm, and relatively uniform groups obtained there is a possibility for inclusion of new deposits into one of these groups and selection of the nearest to it analogous object, that will simplify the design of development system and identify ways and means of improving system’s effectiveness.

In traditional dynamic principal component analysis (DPCA) for fault detection, there are some drawbacks such as an excess of the number of principal components (PCs), low computational efficiency, etc. For dealing with the problem, this paper develops a hybrid dynamic principal component analysis (HDPCA) technique, this method can remove spacial and serial correlation by divide-and-conquer algorithm instead of parallel processing strategy, which can detect individual fault accurately and efficiently. The strip breaking fault in steel rolling process is used to demonstrate the improved performance of developed technique in comparison with traditional DPCA fault detection methods. It can be perceived that HDPCA algorithm has the better performance of fault detection and computational efficiency.

A new methodology is proposed for monitoring multi- and megavariate systems whose variables present significant levels of autocorrelation. The new monitoring statistics are derived after the preliminary generation of decorrelated residuals in a dynamic principal component analysis (DPCA) model. The proposed methodology leads to monitoring statistics with low levels of serial dependency, a feature that is not shared by the original DPCA formulation and that seriously hindered its dissemination in practice, leading to the use of other, more complex, monitoring approaches. The performance of the proposed method is compared with those of a variety of current monitoring methodologies for large-scale systems, under different dynamical scenarios and for different types of process upsets and fault magnitudes. The results obtained clearly indicate that the statistics based on decorrelated residuals from DPCA (DPCA-DR) consistently present superior performances regarding detection ability and decorrelation power and are also robust and efficient to compute.